Find the equation of the circle which passes through the points (1, 2), (2, 2) and (4, -1)?

Asked by Last Modified  

2 Answers

+2 Mathematics Conic Sections

Follow 0
Answer

Please enter your answer

Sarvajeet Kumar

An Experienced Trainer

square of (x-3/2) + square of (y-3/2) = 1/2.
Comments
Dislike Bookmark

Tutor

Take the general equation for a circle: x^2 + y^2 + 2gx + 2fy + c = 0, where the center is at (-g, -f) and the radius is sq root of (g^2 +f^2 -c). Now use the given points to get three equations to solve for three unknowns, g, f, and c. The equations with point (1, 2) becomes: 1^2 + 2^2 + 2xgx1 + 2xfx2...
read more
Take the general equation for a circle: x^2 + y^2 + 2gx + 2fy + c=0, where the center is at (-g, -f) and the radius is sq root of (g^2 +f^2 -c). Now use the given points to get three equations to solve for three unknowns, g, f, and c. The equations with point (1, 2) becomes: 1^2 + 2^2 + 2xgx1 + 2xfx2 + c=0 => 2g + 4f + c=- 5 .............. (1) Similarly, the equation with the point (2, 2) is: => 4g + 4f + c=- 8 .............. (2) And, the equation with the point (4, -1) is: => 8g - 2f + c=- 17 .............. (3) From (1) - (2) we get: -2g = 3 --> g=-3/2. Using this value of g in (1) we get: 4f + c=- 2 ............ (4) Using this value of g in (3) we get: -2f + c=- 5 ............ (5) From (4) - (5) we can get: 6f=3 --> f=1/2. Using this value of f in (5) we get: c=- 4. So, the equation of the circle is: x^2 + y^2 + 2(-3/2)x + 2(1/2)y + (- 4) = 0. After simplification: --> x^2 + y^2 -3x +y - 4 = 0 (Answer) read less
Comments
Dislike Bookmark

Related Questions

What is difference between electric field and electric potential?
Electric field is the measure of the negative gradient of electric potential. Meaning field tells us how much change would occur in potential as we move in space.
Ravi Ranjan
1 0
View Comments8
Mathematically Quantum theory is states as __________. (E = mc2, E = hf, v = nl, none of these)
E = hf
Narendra Kumar
0 0
View Comments7
What are monthly charges for 11 & 12 CBSE students for maths in Baroda?
Perhaps Rs. 1500/- would be adequate.
Er Megha Pandey
I was enrolled to a coaching for 11th and 12th standard. Due to my low performance in JEE advanced I want to give 1 more year to prep. I have all the study material. I am planning to just solve that and join test series. But the problem is how to get my doubts cleared? And will this strategy work?
you can look out for online tutors who can clear your doubts. Also there are many online forums available that can help you with the same. Look out for tricks that are available on Youtube. you can also opt for online test series.
Priyanshu
|z-3-4i|=7 find the locus of z. sol.we know that in argand plane the complex no. is represented with a pt. compare this equation with |z-q|=r whera q is a complex no. (every real no. is also a complex no.)so Q=(3,4) in argand plane .and z is any point on the argand plane. |z-3-4i| represent the distance of point z from pt.(3,4) in the argand plane or complex plane. this distance is also given in the question =7.so the locus of z is any point from pt.(3,4) which is at a distance 7 from point (3,4).which is represnt a circle.because the circle is a curve traced by a moving point which is moving in such a way that it is at a fixed distance from a fixed pt. while moving.
It can be re written in Cartesian form as (x-3)^2 + (y-4)^2 = 7^2 This is equation of a circle with center at (3,4) and radius equal to 7
Sandeep
0 0
View Comments6

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Applications Of Integral Calculus
Integral calculus has a lot of practical applications. It can be used to find the area, surface area, Volume for all geometrical shapes. Area= ∫ydx Volume= ∫Πy2dx Thus for finding area, volume...

Kumaresh Natarajan

0 0
View Comments0
4 Things Every Tech Startup Needs to Know About The Coaching Industry
Knowledge on any subject is widely available to those who wish to learn. However, just gathering knowledge from other people doesn’t guarantee results in business. Results come from applying what...

Rajesh N V

3 0
View Comments1
Class 11: Important Prefixes In The Si System
Mostly commonly terms like "picometre", "nanometre" needs to be converted to SI units to solve in one unit correctly. Micrometre, picometre, nanometre are often used. One can convert them in metres, etc (units).

Nidhi T.

0 0
View Comments0
Introduction To Accounting: Part 13: Money Measurement Concept
According to the Money Measurement Concept, only those transactions and events are recorded in the books of accounts which can be measured in terms of money. Therefore, a transaction which cannot...

Nishant Kumar

0 0
View Comments0
Introduction To Accounting: Part 20: Summary Of Accounting Concepts

Nishant Kumar

0 0
View Comments0

Recommended Articles

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Urmila, an MBBS tutor from Bangalore

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition.  Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Chennai
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Pune
Class 12 Tuition in Jaipur
Class 12 Tuition in Lucknow
Class 12 Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you